How to get mirrored tiling in Cycles?
You can achieve this usign math nodes:
Click for full size


Edit:
I have just seen you can even leave out the modulo operation. I thought it would make the coordinates repeat between 0 and 1 but it just does nothing.

Here is the .blend file for you.

What this node setup does is basically flip the UV coordinates when the image border is reached.

Result (with multiple flips):